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GROUP 2 NAME : 1.USWATUN KHASANAH 2.TIKA NURLAELI 3.SITI AMIDAH 4.NURFETI DWI SUSILOWATI Page 77 7. Identify the hypothesis and conclusion in the following: a. Two lines are parallel if they do not intersect conclusion hypothesis b. All squares are rectangles hypothesis conclusion Page 78 2. Produce a counterexample for the following false generalization. There is only one line perpendicular to a given line at a point on that line. False generalization : There is only one line perpendicular to a given line at a point on that line. Comment : to show that the generalization is false, we must provide not only one line perpendicular to a given line at a point on that line. Counterexample : figure ab and cd are perpendicular, but not only cd which can perpendicular with ab, ef and ab are perpendicular too 4. True – false a. Two points determine a line (true) b. A line separates space into two half-spaces (false) c. If two planes intersect, the intersection is a point (false) d. If X, Y, and Z are collinear and XZ + ZY = XY then Z is between X and Y (true) 5. If B is between A and C, AC = 10, and AB = 4, find BC. Answer: BC = AC – AB = 10 – 4 =6 7. Identify the hypothesis and conclusion in the following statements: a. A triangle is isosceles if it has two congruent sides conclusion hypothesis a. All equilateral triangles have three congruent angles hypothesis conclusion 8. Consider the statement: If two angles are right angles, they are congruent. a. Write the converse statement Answer: If two angles are congruent, they are right angles. b. Write the inverse statement Answer: If two angles are not right angles, they are not congruent. c. Write the contapositive statement Answer: If two angles are not congruent, they are not right angles d. Produce counterexamples to show a and b are false If two angles are congruent, they are right angles. False generalization : If two angles are congruent, they are right angles. Comment : to show that the generalization is false, we must provide two angles are congruent which does not right angle. Counterexample : figure ⦟abc and ⦟klm are congruent but they are not right angle, they are acute angle. c m